Light always travels at the same speed. So, nothing slows it down, not even a black hole.

What mass does is warp space-time. This appears to "bend" light (the light is not actually bending but rather space-time is) that travels past it. Think of a stretched piece of plastic that has a metal ball placed in it. The plastic will dip in towards that ball. A marble rolled in a straight line on the plastic will, when getting near the metal ball, strart curving with the depression of the plastic. So the marble (analogy for a light photon, or could be a planet orbiting a star) is actually travelling in a straight line but the plastic is warped under it.

At the event horizon of a black hole, space-time is warped by the exact amount to prevent light from escaping.